Asymmetric Exponential Power Research Articles

Asymmetric exponential power Bayesian median autoregression with applications

Compared with the widely used mean-based models, the prediction based on median autoregression is often more robust for time series forecasting. Motivated by the asymmetric exponential power working likelihood approach in Bayesian quantile regression, we first apply the asymmetric exponential power error to time series. The new median autoregression we proposed is more robust and can better deal with outliers. An adaptive independent Metropolis-Hastings algorithm is used for the parameter estimation. A novel, simple, and effective approximate forecasting procedure is proposed based on the Watanabe-Akaike information criterion in the framework of Bayesian model averaging. Model assessment, order selection, and out-of-sample predictive accuracy are all discussed. Finally, three examples of macroeconomic data are analyzed to show the superior performance of the proposed model.

A Mixture Autoregressive Model Based on an Asymmetric Exponential Power Distribution

In nonlinear time series analysis, the mixture autoregressive model (MAR) is an effective statistical tool to capture the multimodality of data. However, the traditional methods usually need to assume that the error follows a specific distribution that is not adaptive to the dataset. This paper proposes a mixture autoregressive model via an asymmetric exponential power distribution, which includes normal distribution, skew-normal distribution, generalized error distribution, Laplace distribution, asymmetric Laplace distribution, and uniform distribution as special cases. Therefore, the proposed method can be seen as a generalization of some existing model, which can adapt to unknown error structures to improve prediction accuracy, even in the case of fat tail and asymmetry. In addition, an expectation-maximization algorithm is applied to implement the proposed optimization problem. The finite sample performance of the proposed approach is illustrated via some numerical simulations. Finally, we apply the proposed methodology to analyze the daily return series of the Hong Kong Hang Seng Index. The results indicate that the proposed method is more robust and adaptive to the error distributions than other existing methods.

Does the asymmetric exponential power distribution improve systemic risk measurement?

Does the asymmetric exponential power distribution improve systemic risk measurement?

Robust mixture regression via an asymmetric exponential power distribution

Finite mixture of linear regression (FMLR) models are an efficient tool to fit the unobserved heterogeneous relationships. The parameter estimation of FMLR models is usually based on the normality assumption, but it is very sensitive to outliers. Meanwhile, the traditional robust methods often need to assume a specific error distribution, and are not adaptive to dataset. In this paper, a robust estimation procedure for FMLR models is proposed by assuming that the error terms follow an asymmetric exponential power distribution, including normal distribution, skew-normal distribution, generalized error distribution, Laplace distribution, asymmetric Laplace distribution, and uniform distribution as special cases. The proposed method can select the suitable loss function from a broad class in a data driven fashion. Under some conditions, the asymptotic properties of proposed method are established. In addition, an efficient EM algorithm is introduced to implement the proposed methodology. The finite sample performance of the proposed approach is illustrated via some numerical simulations. Finally, we apply the proposed methodology to analyze a tone perception data.

A Cross-Sectional Analysis of Growth and Profit Rate Distribution: The Spanish Case

We analyse the time evolution of the empirical cross-sectional distribution of firms’ profit and growth rates. In particular, we analyse the conditional properties of the empirical distributions depending on the size of the firms and the business cycle phase. In order to do so, we employ the Laplace distribution as a benchmark, further considering the Subbotin and Asymmetric Exponential Power (AEP hereafter) distributions, to capture the potential asymmetry and leptokurtosis of the empirical distribution. Our results show that the profit rates of large firms are characterised by an asymmetric Laplace distribution with parameters largely independent of the business cycle phase. Small firms, instead, are characterised by the AEP distribution, which accounts for the conditional dependence of distribution on the phase of the business cycle. We observe that the largest firms are more robust to downturns compared to the small firms, given their invariant distributional characteristics during crisis periods.

Risk measurement for conditionally heteroscedastic location-scale time series models with ASTD and AEPD innovations

This study examines the asymptotic properties of a class of conditionally heteroscedastic location-scale time series models with innovations following a generalized asymmetric Student-t distribution (ASTD) or an asymmetric exponential power distribution (AEPD). We first show the consistency and asymptotic normality of the conditional maximum likelihood estimator of the model parameters under certain regularity conditions. Then, based on the maximum likelihood estimator, we estimate conditional value-at-risk (VaR) and expected shortfall (ES) by using their closed forms induced from the model. Their performance is finally compared with that of conditional autoregressive VaR and expectile methods. A simulation study and real data analysis are provided as an illustration.

Critical evaluation of CNA estimators for DNA data using matching confidence masks and WGS technology

A big number of different estimators have been proposed during decades to detect the Copy Number Alterations (CNA) in Deoxyribonucleic Acid (DNA) structures and indicate various diseases, including cancer. Due to the different cost functions and wide variations in DNA probes, the estimates in some cases turn out to be incompatible with each other. Therefore, each DNA profile is often supplied with a ‘gold standard’ provided by medical experts according to their expertise. In this paper, we test various CNAs estimators based on the Whole Genome Sequencing (WGS) and select the best one using probabilistic confidence masks. The masks are created for the segmental Gaussian noise and asymmetric exponential power distribution in the breakpoints. The estimates produced by the algorithms are compared at several probability levels. A complete statistical analysis of the CNA structures is carried out by varying the probability of the breakpoint existence. The best estimator is selected for each of the DNA profiles.

A new risk measurement method for China's carbon market

AbstractCarbon markets were set up with the aim to achieve carbon reduction target and sustainable development. However, market risk has become one of the key factors influencing continuous development of carbon markets. Different from traditional financial asset price, carbon price has a heterogeneous characteristic in its tail distribution. The current value at risk (VaR) model with student t or generalized error distribution (GED) cannot describe the asymmetric tail distribution of carbon price. Therefore, this article propose to develop a combined model for China's carbon market risk measurement. First, extend generalized autoregressive conditional heteroscedasticity (GARCH) with standardized standard asymmetric exponential power distribution (SSAEPD) to reflect volatility clustering phenomenon and heterogeneous distribution character of China's carbon price. Then, genetic algorithm (GA) was innovatively used to solve GARCH‐SSAEPD linear programming instead of interior‐point algorithm. Finally, use VaR to measure the carbon market risk. The new model (GARCH‐SSAEPD‐GA‐VaR) is implied to China's carbon market and compared with the traditional GARCH‐VaR model, the empirical results show: (a) Compared with current VaR framework, the GARCH‐SSAEPD‐GA‐VaR model we constructed can help describe the heterogeneous tail distribution of carbon price and help increase the precision of carbon market risk measurement. (b) SSAEPD can capture fat‐tail, asymmetric effects of China's carbon price more entirely, which puts forward a new method to study the evolvement laws of carbon market risk. (c) GA is effective to achieve global optimum to some extent in parameter estimation. This study contribute to developing theory and methodology of describing particularity features of carbon price, increasing the accuracy of carbon market risk measurement and provide a new perspective for investigating the evolvement regularity of China's carbon market risks.

Value‐at‐risk forecasting via dynamic asymmetric exponential power distributions

AbstractIn the value‐at‐risk (VaR) literature, many existing works assume that the noise distribution is the same over time. To take into account the potential time‐varying dynamics of stock returns, we propose a dynamic asymmetric exponential distribution‐based framework. The new method includes a time‐varying shape parameter to control the dynamic shape of the distribution, a time‐varying probability parameter to control the dynamic proportion of positive returns, and a time‐varying scale parameter to control the dynamic volatility. We combine the generalized method of moments and the exponentially weighted moving average (EWMA) approach to derive specifications for these time‐varying parameters. Empirical applications demonstrate the superior performance of the proposed method when compared with various GARCH and EWMA approaches without time variation in the innovations.

China’s Carbon Pricing Based on Heterogeneous Tail Distribution

To address climate change, the carbon emission trading scheme has become one of the main measures to achieve emission reduction goals. One of the core problems in constructing the carbon emissions trading market is determining carbon emissions trading prices. The scientific nature of carbon emissions pricing determines the effectiveness of market regulation. Research on the influencing factors and heterogeneous tail distribution of carbon prices can increase the accuracy of carbon pricing, which is particularly important for the development of the carbon emissions trading market. The current studies have some limitations and lack heterogeneous tail description. We employ the arbitrage pricing theory-standardized standard asymmetric exponential power distribution model to analyze China’s regional carbon emissions trading price and use a genetic algorithm to solve linear programming. The results confirm the theoretical results and efficiency of the proposed algorithm. First, the new model can capture the skewness, fat-tailed distribution, and asymmetric effects of China’s regional carbon emissions trading price. Second, the macroeconomy, similar products, energy price, and exchange rate influence the carbon price fluctuation; investors’ behavior plays an important role in the heterogeneous tail distribution of carbon price. The findings provide references for the government to take appropriate measures to promote carbon emission reduction and improve the effectiveness of China’s carbon market. Therefore, our findings can help enhance emission reduction and achieve sustainable development of a low-carbon environment.

Wind Power Curve Modeling With Asymmetric Error Distribution

Wind power curves play important roles in developing and utilizing wind energy, including wind power forecasting, wind turbine condition monitoring, wind energy potential estimation, and wind turbine selection. In this paper, we show that the error distribution in wind power curve modeling is asymmetric and complex, rather than a Gaussian distribution. Considering this error characteristic, we develop two novel asymmetric spline regression models, MoAG-ASR and MoAEP-ASR, in which the error terms are assumed to obey mixture of asymmetric Gaussian distributions (MoAG) and mixture of asymmetric exponential power distribution (MoAEP), respectively. We compare the proposed models with 16 popular wind power curve fitting models, and find that the proposed models rank higher than the others. Moreover, besides the asymmetry, two statistics (skewness and kurtosis) also show that the error distribution in wind power curve modeling is thick-tailed and leptokurtic. However, MoAG and MoAEP can precisely fit such complex error distribution. Thus, MoAG-ASR and MoAEP-ASR are effective tools for wind power curve modeling.

Correcting estimates of DNA CNAs using improved confidence masks tuned to gold standard

Copy number alterations (CNAs) are hallmarks of cancer, which are now been routinely measured by different techniques and used for diagnostic and prognostic purpose. Efficient and accurate detection of the breakpoint positions in heterogeneous cancer sample measured with intrinsic random noise and subjected to technical and biological biases is a challenging practical and methodological problem. To improve the CNA estimates, the authors present the probabilistic approach for breakpoints detection that gives confidence masks (the system of local segmentation profiles with confidence probabilities) tuned using experts estimates. The authors show that the asymmetric exponential power distribution matches well the uncertainties (jitter) in the breakpoint locations. The confidence upper and lower boundary masks for the breakpoint location are built using this function. The confidence masks are then tuned based on the medical expert annotations of the training set of the breakpoints obtained by the standard circular binary segmentation (CBS) algorithm. Comparison of modified confidence masks and experts annotations on the testing set of CNA profiles of neuroblastoma showed improvement of the CNA estimates.

Asymmetric competition, risk, and return distribution

We propose a parsimonious statistical model of firm competition where structural differences in the strength of competitive pressure and the magnitude of return fluctuations above and below the system-wide benchmark translate into a skewed Subbotin or asymmetric exponential power (AEP) distribution of returns to capital. Empirical evidence from US data illustrates that the AEP distribution compares favorably to popular alternative models such as the symmetric or asymmetric Laplace density in terms of goodness of fit when entry and exit dynamics of markets are taken into account.

Skewed link-based regression models for misclassified binary data

In this paper, we propose flexible Bayesian approaches for binary regression models in the presence of misclassified data. These approaches consider asymmetric links based on the skew-normal and the asymmetric exponential power distributions. The computational difficulties have been avoided by using data augmentation schemes. The idea of using data augmentation schemes with two types of latent variables is exploited to derive efficient MCMC algorithms. A simulation study and an application illustrate the model performance in comparison with the standard methods that do not consider skewness and/or which do not consider misclassification.

NORTA for portfolio credit risk

We use NORTA (NORmal To Anything) to enhance normal credit-risk factor settings in modeling common risk factors and capturing contagion effects. NORTA extends the multivariate Normal distribution in that it enables the simulation of a random vector with arbitrary and known marginals and correlation structure. NORTA can be solved either by numerical integration (Cario and Nelson in Modeling and generating random vectors with arbitrary marginal distributions and correlation matrix, Technical report, Department of Industrial Engineering and Management Sciences, Northwestern University, IL, 1997) or by Monte Carlo simulation (Ilich in Eur J Oper Res 192(2):468–478, 2009). The former approach, which is the most efficient, assumes that the marginals’ inverse cumulative functions are given, while the latter, which is more flexible but less efficient, does not. We show how to combine both approaches for higher flexibility and efficiency. We solve for NORTA and experiment with Normal, Student, and Asymmetric Exponential Power (AEP) distributions. We match NORTA models to Normal models with the same marginals’ first and second moments. Yet, differences in credit-risk measures can be highly significant. This supports NORTA as a viable alternative for credit-risk modeling and analysis.

Firm dynamics and regional resilience: an empirical evolutionary perspective

This article breaks down the distributional analysis of firm growth rates to the domain of regions. Extreme growth events, i.e., turbulence at the level of firms, are conceptualized as an indicator of competitive regional environments which enable processes like structural adaptation or technological re-orientation. This provides a micro-funded empirical framework to operationalize the evolutionary dimension of regional resilience. Therefore, the flexible Asymmetric Exponential Power density is fitted to firm data for each German region during the years of economic downturn (2008–2010). Results show that firm-level turbulence is more pronounced in regions with higher aggregate growth performance, with a highly qualified workforce and with more unrelated variety in the industrial portfolio.

On entropy-based goodness-of-fit test for asymmetric Student-t and exponential power distributions

ABSTRACTThis paper examines the goodness-of-fit (GOF) test for a generalized asymmetric Student-t distribution (ASTD) and asymmetric exponential power distribution (AEPD). These distributions are known to include a broad class of distribution families and are quite suitable to modelling the innovations of financial time series. Despite their popularity, to our knowledge, no studies in the literature have so far investigated their affinity and differences in implementation. To fill this gap, we examine the empirical power behaviour of entropy-based GOF tests for hypotheses wherein the ASTD and AEPD play the role of null and alternative distributions. Our findings through a simulation study and real data analysis indicate that the two distributions are generally hard to distinguish and that the ASTD family accommodates AEPDs to a greater degree than the other way around for larger samples.

On the flexibility of GARCH-family models with an application to the BRICS stock indices

ABSTRACTFinancial asset returns are known to exhibit fatter tails with substantial skewness and high kurtosis due to volatility. In this article, the dynamics of implied volatility of BRICS indices are described using 10 GARCH-type models. The innovation processes of these GARCH models are characterized using 13 parametric distributions, including these 4 uncommon, flexible ones: Student's t-gamma mixture, normal-gamma mixture, asymmetric exponential power, and generalized asymmetric student's t distributions. The performance and predictive ability of these GARCH models are evaluated in terms of value at risk and expected shortfall with some loss functions. The EST-GARCH with error distribution based on the asymmetric exponential power distribution gives the best fit.

A New Fama-French 5-Factor Model Based on SSAEPD Error and GARCH-Type Volatility

In this paper, we extend the 5-factor model in Fama and French (2015) with the non-Normal errors distribution of SSAEPD (Standardized Standard Asymmetric Exponential Power Distribution) in Zhu and Zinde-Walsh (2009) and the GARCH-type volatility. The focus is on finding out whether our new model can outperform the original Fama-French 5-factor model. We use Fama-French 25 value-weighted portfolios to conduct our research. The MLE is used to estimate the parameters. The LR test and KS test are used for model diagnostics. Models are compared by AIC. Empirical results show that with GARCH-type volatilities and non-normal errors, the Fama-French 5 factors are still alive. Our new model can successfully capture the skewness, fat-tailness and asymmetric kurtosis in the data and has better in-sample fit than the 5-factors model in Fama and French (2015). Our study provides an update to existing asset pricing literature and reference for investors.

The patterns of Chinese firm growth: a conditional estimation approach of the asymmetric exponential power density

This article investigates the impact of ownership type on the entire growth rate distributional mass of Chinese firms, using a conditional estimation approach of the asymmetric exponential power density that goes beyond simple location-shift analysis. We first find a Chinese growth puzzle, i.e. a deviation from the stylized fact of the variance-scaling relationship commonly observed in Western European economies. We then find that the ownership type mainly affects growth rates far-off the mean value. Our results also indicate that barriers to becoming a high growth firm, such as financial constraints, are especially prevalent in the Chinese private sector